occ::dft Namespace Reference

functionality related to Kohn-Sham density functional theory More...

Namespaces
namespace	cosx
namespace	grid
namespace	impl
namespace	kernels

Classes
struct	AtomGrid
	Structure to hold atom-centered grid data. More...
class	DensityFunctional
class	DFT
struct	DFTMethod
struct	FuncComponent
class	HirshfeldPartition
	Class implementing Hirshfeld atomic charge analysis. More...
struct	MethodDefinition
class	MolecularGrid
	Class for molecular integration grids in DFT. More...
class	MolecularGridPoints
	Class for storing and managing molecular grid points. More...
class	NonLocalCorrelationFunctional
struct	PartitionMethod
struct	RadialGrid
	Structure to hold radial grid data. More...
struct	RangeSeparatedParameters

Typedefs
using	PointChargeList = std::vector< occ::core::PointCharge >
using	dfid = DensityFunctional::Identifier

Enumerations
enum class	PartitionFunction { Becke , StratmannScuseria }
	Enumeration of available partition functions for atomic weight calculation. More...
enum class	RadialGridMethod {   LMG , TreutlerAlrichs , MuraKnowles , Becke ,   GaussChebyshev , EulerMaclaurin }
	Enumeration of available radial grid generation methods. More...

Functions
DFTMethod	get_dft_method (const std::string &method_string)
DFTMethod	create_dft_method_from_definition (const MethodDefinition &def, bool polarized=false)
ankerl::unordered_dense::map< std::string, MethodDefinition >	load_method_definitions (const std::string &filename)
void	export_method_definitions (const std::string &filename, const ankerl::unordered_dense::map< std::string, MethodDefinition > &definitions)
std::string	dfid_to_string (DensityFunctional::Identifier id)
DensityFunctional::Identifier	string_to_dfid (const std::string &name)
uint_fast16_t	nearest_grid_level_at_or_above (uint_fast16_t n)
	Find the nearest Lebedev grid level at or above the requested number of points.
uint_fast16_t	nearest_grid_level_below (uint_fast16_t n)
	Find the nearest Lebedev grid level below the requested number of points.
size_t	angular_point_count (size_t level)
	Get the number of points in a Lebedev grid.
double	get_atomic_radius (size_t atomic_number)
	Get the atomic radius for a given atomic number.
Vec	becke_partition (const Vec &w)
	Apply the Becke partition function.
Vec	stratmann_scuseria_partition (const Vec &w)
	Apply the Stratmann-Scuseria partition function.
Mat	calculate_interatomic_distances (const Mat3N &positions)
	Calculate interatomic distances.
Mat	calculate_atomic_grid_weights (PartitionMethod method, const Mat &grid_points, const Mat &atomic_positions, const Vec &radii, const Mat &interatomic_distances)
	Calculate Becke atomic weights for grid points.
IVec	prune_nwchem_scheme (size_t nuclear_charge, size_t max_angular, size_t num_radial, const Vec &radii)
	Apply the NWChem pruning scheme to a radial grid.
IVec	prune_numgrid_scheme (size_t atomic_number, size_t max_angular, size_t min_angular, const Vec &radii)
	Apply the NumGrid pruning scheme to a radial grid.
RadialGrid	generate_becke_radial_grid (size_t num_points, double rm=1.0)
	Generate a Becke radial grid.
RadialGrid	generate_mura_knowles_radial_grid (size_t num_points, size_t charge)
	Generate a Mura-Knowles radial grid.
RadialGrid	generate_treutler_alrichs_radial_grid (size_t num_points)
	Generate a Treutler-Alrichs radial grid.
RadialGrid	generate_gauss_chebyshev_radial_grid (size_t num_points)
	Generate a Gauss-Chebyshev radial grid.
RadialGrid	generate_euler_maclaurin_radial_grid (size_t num_points, double alpha)
	Generate a Euler-Maclaurin radial grid.
RadialGrid	generate_lmg_radial_grid (size_t atomic_number, double radial_precision, double alpha_max, int l_max, const occ::Vec &alpha_min)
	Generate a Lindh-Malmqvist-Gagliardi (LMG) radial grid.
double	lmg_inner (const double max_error, const double alpha_inner)
	Helper function to calculate LMG inner radial boundary.
double	lmg_outer (const double max_error, const double alpha_outer, const int l, const double guess)
	Helper function to calculate LMG outer radial boundary.
double	lmg_h (const double max_error, const int l, const double guess)
	Helper function to calculate LMG grid spacing parameter.
AtomGrid	generate_atom_grid (size_t atomic_number, const GridSettings &settings, RadialGridMethod method=RadialGridMethod::LMG, double alpha_max=0.0, int l_max=0, const Vec &alpha_min=Vec())
	Generate an atom-centered grid using the specified method.
Vec	calculate_hirshfeld_charges (const occ::qm::AOBasis &basis, const occ::qm::MolecularOrbitals &mo, int charge=0)
	Calculate Hirshfeld charges for a molecule.
std::vector< occ::core::Multipole< 4 > >	calculate_hirshfeld_multipoles (const occ::qm::AOBasis &basis, const occ::qm::MolecularOrbitals &mo, int max_multipole_order=4, int charge=0)
	Calculate Hirshfeld multipoles for a molecule.
template<occ::qm::SpinorbitalKind spinorbital_kind, int derivative_order>
void	xc_potential_matrix (const DensityFunctional::Result &res, MatConstRef rho, const occ::gto::GTOValues &gto_vals, MatRef KK, double &energy)=delete
template<>
void	xc_potential_matrix< Restricted, 0 > (const DensityFunctional::Result &res, MatConstRef rho, const occ::gto::GTOValues &gto_vals, MatRef KK, double &energy)
template<>
void	xc_potential_matrix< Restricted, 1 > (const DensityFunctional::Result &res, MatConstRef rho, const occ::gto::GTOValues &gto_vals, MatRef KK, double &energy)
template<>
void	xc_potential_matrix< Restricted, 2 > (const DensityFunctional::Result &res, MatConstRef rho, const occ::gto::GTOValues &gto_vals, MatRef KK, double &energy)
template<>
void	xc_potential_matrix< Unrestricted, 0 > (const DensityFunctional::Result &res, MatConstRef rho, const occ::gto::GTOValues &gto_vals, MatRef KK, double &energy)
template<>
void	xc_potential_matrix< Unrestricted, 1 > (const DensityFunctional::Result &res, MatConstRef rho, const occ::gto::GTOValues &gto_vals, MatRef KK, double &energy)
template<>
void	xc_potential_matrix< Unrestricted, 2 > (const DensityFunctional::Result &res, MatConstRef rho, const occ::gto::GTOValues &gto_vals, MatRef KK, double &energy)

Variables
const std::array< uint_fast16_t, 33 >	lebedev_grid_levels
	Array of available Lebedev grid levels.

Detailed Description

functionality related to Kohn-Sham density functional theory

part of the occ::qm, occ:gto, occ:io module

Typedef Documentation

dfid

using occ::dft::dfid = typedef DensityFunctional::Identifier

PointChargeList

using occ::dft::PointChargeList = typedef std::vector<occ::core::PointCharge>

Enumeration Type Documentation

PartitionFunction

enum class occ::dft::PartitionFunction

strong

Enumeration of available partition functions for atomic weight calculation.

Enumerator
Becke	Becke's original partition function.
StratmannScuseria	Stratmann-Scuseria partition function.

RadialGridMethod

enum class occ::dft::RadialGridMethod

strong

Enumeration of available radial grid generation methods.

Enumerator
LMG	Lindh-Malmqvist-Gagliardi method.
TreutlerAlrichs	Treutler-Alrichs method.
MuraKnowles	Mura-Knowles method.
Becke	Becke's transformation method.
GaussChebyshev	Gauss-Chebyshev method.
EulerMaclaurin	Gauss-Chebyshev method.

Function Documentation

angular_point_count()

size_t occ::dft::angular_point_count

(

size_t

level

)

Get the number of points in a Lebedev grid.

Parameters

level

The Lebedev grid level

Returns

size_t The number of points in the grid

becke_partition()

Vec occ::dft::becke_partition

(

const Vec &

w

)

Apply the Becke partition function.

Parameters

w	Input values to partition

Returns

Vec Partitioned values

calculate_atomic_grid_weights()

Mat occ::dft::calculate_atomic_grid_weights	(	PartitionMethod	method,
		const Mat &	grid_points,
		const Mat &	atomic_positions,
		const Vec &	radii,
		const Mat &	interatomic_distances
	)

Calculate Becke atomic weights for grid points.

Parameters

grid_points	Grid points (3 x N)
atomic_positions	Atomic positions (3 x M)
radii	atomic radii (M)
interatomic_distances	Matrix of interatomic distances (M x M)

Returns

Mat Matrix of weights (N x M)

calculate_hirshfeld_charges()

Vec occ::dft::calculate_hirshfeld_charges	(	const occ::qm::AOBasis &	basis,
		const occ::qm::MolecularOrbitals &	mo,
		int	charge = 0
	)

Calculate Hirshfeld charges for a molecule.

Convenience function to compute Hirshfeld charges in a single call.

Parameters

basis	Basis set for the molecule
mo	Molecular orbitals containing the density matrix
charge	Total molecular charge

Returns

Vec Vector of Hirshfeld charges for each atom

calculate_hirshfeld_multipoles()

std::vector< occ::core::Multipole< 4 > > occ::dft::calculate_hirshfeld_multipoles	(	const occ::qm::AOBasis &	basis,
		const occ::qm::MolecularOrbitals &	mo,
		int	max_multipole_order = 4,
		int	charge = 0
	)

Calculate Hirshfeld multipoles for a molecule.

Convenience function to compute Hirshfeld multipoles in a single call.

Parameters

basis	Basis set for the molecule
mo	Molecular orbitals containing the density matrix
max_multipole_order	Maximum order of multipoles to compute (0-4)
charge	Total molecular charge

Returns

std::vector<occ::core::Multipole<4>> Vector of Hirshfeld multipoles for each atom

calculate_interatomic_distances()

Mat occ::dft::calculate_interatomic_distances

(

const Mat3N &

positions

)

Calculate interatomic distances.

Parameters

positions

Atomic positions (3 x N)

Returns

Mat Matrix of interatomic distances

create_dft_method_from_definition()

DFTMethod occ::dft::create_dft_method_from_definition	(	const MethodDefinition &	def,
		bool	polarized = false
	)

dfid_to_string()

std::string occ::dft::dfid_to_string

(

DensityFunctional::Identifier

id

)

export_method_definitions()

void occ::dft::export_method_definitions	(	const std::string &	filename,
		const ankerl::unordered_dense::map< std::string, MethodDefinition > &	definitions
	)

generate_atom_grid()

AtomGrid occ::dft::generate_atom_grid	(	size_t	atomic_number,
		const GridSettings &	settings,
		RadialGridMethod	method = RadialGridMethod::LMG,
		double	alpha_max = 0.0,
		int	l_max = 0,
		const Vec &	alpha_min = Vec()
	)

Generate an atom-centered grid using the specified method.

Parameters

atomic_number	Atomic number of the center atom
settings	Grid generation settings
method	The radial grid method to use
alpha_max	Maximum exponent from basis set (optional)
l_max	Maximum angular momentum from basis set (optional)
alpha_min	Minimum exponents for each angular momentum (optional)

Returns

AtomGrid The generated atom-centered grid

generate_becke_radial_grid()

RadialGrid occ::dft::generate_becke_radial_grid	(	size_t	num_points,
		double	rm = 1.0
	)

Generate a Becke radial grid.

Reference: A. D. Becke, J. Chem. Phys. 88, 2547 (1988)

Parameters

num_points	Number of radial points
rm	Scaling parameter

Returns

RadialGrid The generated radial grid

generate_euler_maclaurin_radial_grid()

RadialGrid occ::dft::generate_euler_maclaurin_radial_grid	(	size_t	num_points,
		double	alpha
	)

Generate a Euler-Maclaurin radial grid.

Parameters

num_points	Number of radial points
alpha

Returns

RadialGrid The generated radial grid

generate_gauss_chebyshev_radial_grid()

RadialGrid occ::dft::generate_gauss_chebyshev_radial_grid

(

size_t

num_points

)

Generate a Gauss-Chebyshev radial grid.

Parameters

num_points

Number of radial points

Returns

RadialGrid The generated radial grid

generate_lmg_radial_grid()

RadialGrid occ::dft::generate_lmg_radial_grid	(	size_t	atomic_number,
		double	radial_precision,
		double	alpha_max,
		int	l_max,
		const occ::Vec &	alpha_min
	)

Generate a Lindh-Malmqvist-Gagliardi (LMG) radial grid.

Reference: T. Helgaker, P. Jørgensen, J. Olsen, "Molecular Electronic Structure Theory", John Wiley & Sons, 2000

Parameters

atomic_number	Atomic number
radial_precision	Precision parameter for the radial grid
alpha_max	Maximum exponent
l_max	Maximum angular momentum
alpha_min	Minimum exponents for each angular momentum

Returns

RadialGrid The generated radial grid

generate_mura_knowles_radial_grid()

RadialGrid occ::dft::generate_mura_knowles_radial_grid	(	size_t	num_points,
		size_t	charge
	)

Generate a Mura-Knowles radial grid.

Reference: M. E. Mura and P. J. Knowles, J. Chem. Phys. 104, 9848 (1996)

Parameters

num_points	Number of radial points
charge	Atomic number

Returns

RadialGrid The generated radial grid

generate_treutler_alrichs_radial_grid()

RadialGrid occ::dft::generate_treutler_alrichs_radial_grid

(

size_t

num_points

)

Generate a Treutler-Alrichs radial grid.

Reference: O. Treutler and R. Ahlrichs, J. Chem. Phys. 102, 346 (1995)

Parameters

num_points

Number of radial points

Returns

RadialGrid The generated radial grid

get_atomic_radius()

double occ::dft::get_atomic_radius

(

size_t

atomic_number

)

Get the atomic radius for a given atomic number.

Parameters

atomic_number

The atomic number

Returns

double The atomic radius in Bohr

get_dft_method()

DFTMethod occ::dft::get_dft_method

(

const std::string &

method_string

)

lmg_h()

double occ::dft::lmg_h	(	const double	max_error,
		const int	l,
		const double	guess
	)

Helper function to calculate LMG grid spacing parameter.

Parameters

max_error	Maximum error parameter
l	Angular momentum
guess	Initial guess for the spacing

Returns

double Grid spacing parameter

lmg_inner()

double occ::dft::lmg_inner	(	const double	max_error,
		const double	alpha_inner
	)

Helper function to calculate LMG inner radial boundary.

Parameters

max_error	Maximum error parameter
alpha_inner	Inner alpha parameter

Returns

double Inner radial boundary

lmg_outer()

double occ::dft::lmg_outer	(	const double	max_error,
		const double	alpha_outer,
		const int	l,
		const double	guess
	)

Helper function to calculate LMG outer radial boundary.

Parameters

max_error	Maximum error parameter
alpha_outer	Outer alpha parameter
l	Angular momentum
guess	Initial guess for the boundary

Returns

double Outer radial boundary

load_method_definitions()

ankerl::unordered_dense::map< std::string, MethodDefinition > occ::dft::load_method_definitions

(

const std::string &

filename

)

nearest_grid_level_at_or_above()

uint_fast16_t occ::dft::nearest_grid_level_at_or_above

(

uint_fast16_t

n

)

Find the nearest Lebedev grid level at or above the requested number of points.

Parameters

n	Requested number of angular points

Returns

uint_fast16_t The actual number of angular points in the Lebedev grid

nearest_grid_level_below()

uint_fast16_t occ::dft::nearest_grid_level_below

(

uint_fast16_t

n

)

Find the nearest Lebedev grid level below the requested number of points.

Parameters

n	Requested number of angular points

Returns

uint_fast16_t The actual number of angular points in the Lebedev grid

prune_numgrid_scheme()

IVec occ::dft::prune_numgrid_scheme	(	size_t	atomic_number,
		size_t	max_angular,
		size_t	min_angular,
		const Vec &	radii
	)

Apply the NumGrid pruning scheme to a radial grid.

Parameters

atomic_number	Atomic number
max_angular	Maximum number of angular points
min_angular	Minimum number of angular points
radii	Radial grid points

Returns

IVec Number of angular points for each radial point

prune_nwchem_scheme()

IVec occ::dft::prune_nwchem_scheme	(	size_t	nuclear_charge,
		size_t	max_angular,
		size_t	num_radial,
		const Vec &	radii
	)

Apply the NWChem pruning scheme to a radial grid.

Parameters

nuclear_charge	Atomic number
max_angular	Maximum number of angular points
num_radial	Number of radial points
radii	Radial grid points

Returns

IVec Number of angular points for each radial point

stratmann_scuseria_partition()

Vec occ::dft::stratmann_scuseria_partition

(

const Vec &

w

)

Apply the Stratmann-Scuseria partition function.

Parameters

w	Input values to partition

Returns

Vec Partitioned values

string_to_dfid()

DensityFunctional::Identifier occ::dft::string_to_dfid

(

const std::string &

name

)

xc_potential_matrix()

template<occ::qm::SpinorbitalKind spinorbital_kind, int derivative_order>

void occ::dft::xc_potential_matrix ( const DensityFunctional::Result &  res, MatConstRef  rho, const occ::gto::GTOValues &  gto_vals, MatRef  KK, double &  energy  )

delete

xc_potential_matrix< Restricted, 0 >()

template<>

void occ::dft::xc_potential_matrix< Restricted, 0 >	(	const DensityFunctional::Result &	res,
		MatConstRef	rho,
		const occ::gto::GTOValues &	gto_vals,
		MatRef	KK,
		double &	energy
	)

xc_potential_matrix< Restricted, 1 >()

template<>

void occ::dft::xc_potential_matrix< Restricted, 1 >	(	const DensityFunctional::Result &	res,
		MatConstRef	rho,
		const occ::gto::GTOValues &	gto_vals,
		MatRef	KK,
		double &	energy
	)

xc_potential_matrix< Restricted, 2 >()

template<>

void occ::dft::xc_potential_matrix< Restricted, 2 >	(	const DensityFunctional::Result &	res,
		MatConstRef	rho,
		const occ::gto::GTOValues &	gto_vals,
		MatRef	KK,
		double &	energy
	)

xc_potential_matrix< Unrestricted, 0 >()

template<>

void occ::dft::xc_potential_matrix< Unrestricted, 0 >	(	const DensityFunctional::Result &	res,
		MatConstRef	rho,
		const occ::gto::GTOValues &	gto_vals,
		MatRef	KK,
		double &	energy
	)

xc_potential_matrix< Unrestricted, 1 >()

template<>

void occ::dft::xc_potential_matrix< Unrestricted, 1 >	(	const DensityFunctional::Result &	res,
		MatConstRef	rho,
		const occ::gto::GTOValues &	gto_vals,
		MatRef	KK,
		double &	energy
	)

xc_potential_matrix< Unrestricted, 2 >()

template<>

void occ::dft::xc_potential_matrix< Unrestricted, 2 >	(	const DensityFunctional::Result &	res,
		MatConstRef	rho,
		const occ::gto::GTOValues &	gto_vals,
		MatRef	KK,
		double &	energy
	)

Variable Documentation

lebedev_grid_levels

const std::array<uint_fast16_t, 33> occ::dft::lebedev_grid_levels

extern

Array of available Lebedev grid levels.

Each element in the array represents a valid number of Lebedev grid points.